Mathematics that can change the world

Today, much of society’s progress depends on mathematics – everything comes down to calculations.

Mathematics is the foundation of many technological advances and a vast field of research. Mats G Larson, professor of applied mathematics, works at the intersection of mathematics and engineering. His research becomes reality when mathematical formulas are implemented in computers and transformed into powerful tools for simulation and analysis.

“Even though the research is theoretical in nature, the goal is always to solve practical problems. Today, much of society’s progress depends on mathematics – everything comes down to calculations,” he says.

Mats focuses on simulating physical effects using mathematical models. These models help us understand and improve complex systems. If you're designing a car, for example, you probably want it to be strong, lightweight and aerodynamic to reduce energy consumption. You want it to be as optimal as possible, given certain constraints.

“Before engineers build the car in real life, they want to create it virtually – inside a computer. The more they can learn about how the different parts work and optimise function and form before anything is physically built, the more efficient the whole process becomes,” he explains.

Equations explain reality

Fundamental physical phenomena – such as forces, velocity, waves and energy – are often described using partial differential equations. These equations are key to understanding how three-dimensional systems change over time and space, for example how air flows across a car’s body, how fluids move, how waves travel across a surface, or how an elastic material behaves.

Mats develops computer-based methods to solve these equations efficiently. It’s not just about crunching numbers – it also involves geometry and processing large amounts of data. A car, for instance, consists of countless interconnected parts. His methods can also be applied in more complex contexts, such as urban planning. You might want to simulate how an industrial accident affects surrounding areas by modelling how the wind spreads hazardous chemicals.

Methods used by large companies

The methods Mats G Larson has developed to generate physical models have made a strong impact, both scientifically and commercially. Today, large tech companies as well as innovative startups are using the techniques developed by him and his colleagues to build new software.

To understand where it all started, we go back to Chalmers University of Technology in Gothenburg, where Mats studied mechanical engineering, aiming for a career in industry. After graduating, he did his military service in cryptology at the Swedish National Defence Radio Establishment, still without plans for an academic career. But the experience sparked his interest in mathematics, and as the job market was weak at the time, Mats decided to return to Chalmers for a PhD instead of applying for engineering jobs.

“That’s when I started working on what I’m doing now. I was lucky to join a leading research group focusing on computer-based methods for solving partial differential equations – and one thing led to another. Later, I became a postdoc at Stanford University in the US, where I got the chance to work with some of the world’s top researchers,” he says.

Started research collaborations

After a time as professor at Chalmers, he was attracted to Umeå University by strong employment conditions and the opportunity to build a new research environment. In the early years, he collaborated closely with other departments. He helped establish IceLab (Integrated Science Lab), which brings together researchers from the life sciences, as well as the UMIT research lab.

Now in his twenty-first year at Umeå University, Mats G Larson’s research area is more relevant than ever, as mathematics and simulation grow increasingly important.

Recently, his focus has shifted towards artificial intelligence (AI), and how AI can benefit from simulations.

“To train a robot to move over obstacles using AI, for example, you need a simulator. AI, which is essentially just code, needs to interact with a physical system to test different strategies. By adjusting control signals and observing the results, it can optimise the robot’s components and movements to be as efficient as possible,” he says.

The next step is to be able to ask AI questions during the process and get help tailoring a product to different conditions or new requirements. That places high demands on simulation technology and mathematical models – precisely Mats’s area of expertise.

“AI will have huge impact”

“I believe AI will have a huge impact on engineering – and on many other fields – in combination with digitalisation and mathematics. We’ll see a dramatic increase in efficiency in areas like finance, organisational management and text processing, which will have major effects. This makes collaboration between researchers and industry even more exciting.”

Looking ahead, Mats G Larson believes mathematics will continue to play a growing role in society.

“Mathematics is driving large parts of the digital economy. The reason it’s become so influential is that so many things are now controlled digitally. That’s what makes it possible to use maths to solve problems. A lot of it is still quite primitive, but I think this is just the beginning,” he says.